Extremum seeking control apparatus and method for automatic frequency tuning for RF impedance matching

ABSTRACT

A radio frequency (RF) generator includes a RF power source configured to generate an output signal at an output frequency. The RF generator includes a frequency tuning module. The frequency tuning module generates a frequency control signal that controls the output frequency of the RF power source. The frequency control signal includes a frequency tuning signal component and a perturbation signal component. The perturbation signal varies an electrical parameter of the output signal. The frequency tuning signal is adjusted in accordance with a change in output signal in response to the perturbation signal.

FIELD

The present disclosure relates to RF generator systems and control of RFgenerators.

BACKGROUND

The background description provided herein is for the purpose ofgenerally presenting the context of the disclosure. Work of thepresently named inventors, to the extent the work is described in thisbackground section, as well as aspects of the description that may nototherwise qualify as prior art at the time of filing, are neitherexpressly nor impliedly admitted as prior art against the presentdisclosure.

Plasma etching is frequently used in semiconductor fabrication. Inplasma etching, ions are accelerated by an electric field to etchexposed surfaces on a substrate. In one basic implementation, theelectric field is generated based on Radio Frequency (RF) or DirectCurrent (DC) power signals generated by a respective RF or DC generatorof a power delivery system. The power signals generated by the generatormust be precisely controlled to effectively execute plasma etching.

SUMMARY

A radio frequency (RF) generator includes a RF power source configuredto generate an output signal at an output frequency. The RF generatoralso includes a frequency tuning module configured to generate afrequency control signal, the frequency control signal varying theoutput frequency of the RF power source. The frequency control signalincludes a frequency tuning signal component and a perturbation signalcomponent. The perturbation signal varies an electrical parameter of theoutput signal, and the frequency tuning signal is adjusted in accordancewith a change in output signal in response to the perturbation signal.

A radio frequency (RF) generator includes a RF power source configuredto generate an output signal at an output frequency. A frequencycontroller is configured to generate a frequency control signal, wherethe frequency control signal varies the output frequency of the RF powersource. The frequency control signal includes an impedance tuning signalcomponent and a perturbation signal component. A signal source isconfigured to generate the perturbation signal. A mixer is configured tomix the perturbation signal and an electrical parameter to generate amixed signal. A feedback module is configured to determine an updatedfrequency tuning signal in accordance with the mixed signal. A signalcombiner is configured to combine the perturbation signal and theupdated frequency tuning signal and to generate an updated frequencycontrol signal. The perturbation signal varies an electrical parameterof the output signal, and wherein the frequency tuning signal isadjusted in accordance with a change in output signal in response to theperturbation signal. The electrical parameter is at least one ofvoltage, current, forward power, reflected power, or a reflectioncoefficient.

A method for controlling a radio frequency (RF) generator includesgenerating an output signal at an output frequency. The method furtherincludes generating a frequency control signal, the frequency controlsignal varying the output frequency of the RF power source, thefrequency control signal including a frequency tuning signal componentand a perturbation signal component. The perturbation signal varies anelectrical parameter of the output signal, and wherein the frequencytuning signal is adjusted in accordance with a change in output signalin response to the perturbation signal.

Further areas of applicability of the present disclosure will becomeapparent from the detailed description, the claims and the drawings. Thedetailed description and specific examples are intended for purposes ofillustration only and are not intended to limit the scope of thedisclosure.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 depicts a schematic block diagram of a power delivery system formultiple power supplies arranged in accordance with the presentdisclosure;

FIG. 2 depicts a schematic block diagram of a control systemimplementing a conventional feedback-based control of a power supply;

FIG. 3 depicts a Smith Chart on which is plotted a reflectioncoefficient translating to a desired operating condition at the centerof the Smith Chart;

FIG. 4 depicts a Smith Chart on which is plotted a reflectioncoefficient showing zero crossing of the imaginary axis and an optimaltuning position off of the imaginary axis;

FIG. 5 depicts a Smith Chart on which is plotted a reflectioncoefficient showing multiple zero crossings of the imaginary axis;

FIG. 6 depicts a plot of a cost function responsive to sinusoidal inputperturbations for determining a maximum of the cost function;

FIG. 7 depicts a schematic block diagram of a control system having asinusoidal perturbation signal and a response;

FIG. 8 depicts waveforms describing the operation of the block diagramof FIG. 7;

FIG. 9 depicts a block diagram of a RF control system arranged inaccordance with the principles of the present disclosure;

FIG. 10 depicts a plot of waveforms the magnitude of the reflectioncoefficient versus frequency of a RF control system in accordance withthe principles of the present disclosure;

FIG. 11 depicts a plot of frequency versus time of a RF control systemin accordance with the principles of the present disclosure;

FIG. 12 depicts a plot of the reflection coefficient versus frequency ofa RF control system in accordance with the principles of the presentdisclosure;

FIG. 13 depicts a Smith chart of a reflection coefficient of a RFcontrol system according to various embodiments;

FIG. 14 depicts a plot of the magnitude of a reflection coefficientcorresponding versus frequency of a RF control system in accordance withthe principles of the present disclosure;

FIG. 15 depicts a plot of output frequency versus time of a RF controlsystem in accordance with the principles of the present disclosure;

FIG. 16 depicts a functional block diagram of an example control modulearranged in accordance with various embodiments;

FIG. 17 depicts a flow chart of operation of a control system arrangedin accordance with the principles of the present disclosure;

FIG. 18 depicts a flow chart for updating the frequency tuner inaccordance with the principles of the present disclosure;

FIG. 19 depicts a flow chart for updating a cost threshold in accordancewith the principles of the present disclosure;

FIG. 20 depicts a flow chart for updating a cost threshold in accordancewith the principles of the present disclosure;

FIG. 21 depicts a flow chart for updating a cost threshold in accordancewith the principles of the present disclosure; and

FIG. 22 depicts a flow chart for updating a cost threshold in accordancewith the principles of the present disclosure.

In the drawings, reference numbers may be reused to identify similarand/or identical elements.

DESCRIPTION

A power system may include a DC or RF power generator, a matchingnetwork, and a load (e.g., a plasma chamber). The power generatorgenerates a DC or RF power signal, which is received by the matchingnetwork or impedance optimizing controller or circuit. The matchingnetwork or impedance optimizing controller or circuit matches an inputimpedance of the matching network to a characteristic impedance of atransmission line between the power generator and the matching network.This impedance matching aids in maximizing an amount of power forwardedto the matching network (“forward power”) and minimizing an amount ofpower reflected back from the matching network to the power generator(“reverse power”). Forward power may be maximized and reverse power maybe minimized when the input impedance of the matching network matchesthe characteristic impedance of the transmission line.

In the power source or power supply field, there are typically twoapproaches to applying a power signal to the load. A first, moretraditional approach is to apply a continuous power signal to the load.In a continuous mode, a continuous power signal is typically a constantDC or RF sinusoidal power signal that is output continuously by thepower source to the load. In the continuous mode approach, the powersignal assumes a constant DC or sinusoidal output, and the amplitude ofthe power signal and/or frequency (of a RF power signal) can be variedin order to vary the output power applied to the load.

A second approach to applying the power signal to the load involvespulsing the power signal, rather than applying a continuous power signalto the load. In a pulse mode of operation, a power signal is modulatedby a modulation signal in order to define an envelope for the modulatedpower signal. In a conventional pulse modulation scheme, the powersignal typically remains at a constant amplitude and, for RF signals, aconstant frequency. Power delivered to the load is varied by varying themodulation signal, rather than varying the power signal.

In a typical power supply configuration, output power applied to theload is determined by using sensors that measure the forward andreflected power or the voltage and current of the RF signal applied tothe load. Either set of these signals is analyzed in a control loop. Theanalysis typically determines a power value which is used to adjust theoutput of the power supply in order to vary the power applied to theload. In a power delivery system where the load is a plasma chamber orother non-linear load, the varying impedance of the load causes acorresponding varying of power applied to the load, as applied power isin part a function of the impedance of the load.

In plasma systems, power is typically delivered in one of twoconfigurations. In a first configuration, the power is capacitivelycoupled to the plasma chamber. Such systems are referred to ascapacitively coupled plasma (CCP) systems. In a second configuration,the power is inductively coupled to the plasma chamber. Such systems aretypically referred to as inductively coupled plasma (ICP) systems.Plasma delivery systems may include a bias power and/or a source powerapplied to one or a plurality of electrodes. The source power typicallygenerates the plasma and controls plasma density, and the bias powermodulates ions in the formulation of the sheath. The bias and the sourcemay share the same electrode or may use separate electrodes, inaccordance with various design considerations.

When a power delivery system drives a non-linear load, such as a plasmachamber, the power absorbed by the plasma sheath results in a density ofions with a range of ion energy. One characteristic measure of ionenergy is the ion energy distribution function (IEDF). The ion energydistribution function (IEDF) can be controlled with the bias power. Oneway of controlling the IEDF for a system in which multiple RF powersignals are applied to the load occurs by varying multiple RF signalsthat are related by frequency and phase. The frequencies between themultiple RF power signals may be locked, and the relative phase betweenthe multiple RF signals may also be locked. Examples of such systems canbe found with reference to U.S. Pat. Nos. 7,602,127; 8,110,991; and8,395,322, all assigned to the assignee of the present invention andincorporated by reference in this application.

Plasma processing systems may also include components for plasmageneration and control. One such component is a non-linear load, such asa plasma chamber or reactor. A typical plasma chamber or reactorutilized in plasma processing systems, such as by way of example, forthin-film manufacturing, can utilize a dual frequency system. One powergenerator (the source) controls the generation of the plasma, and thepower generator (the bias) controls ion energy. Examples of dual powersystems include systems that are described in U.S. Pat. Nos. 7,602,127;8,110,991; and 8,395,322, referenced above. The dual power systemdescribed in the above-referenced patents requires a closed-loop controlsystem to adapt power supply operation for the purpose of controllingion density and its corresponding ion energy distribution function(IEDF).

Multiple approaches exist for controlling a plasma chamber forgenerating plasmas. For example, in RF power delivery systems, phase andfrequency of the driving RF signals may be used to control plasmageneration. For RF driven plasma sources, the periodic waveformaffecting plasma sheath dynamics and the corresponding ion energy aregenerally known and are controlled by the frequency of the periodicwaveforms and the associated phase interaction. Another approach in RFpower delivery systems involves dual frequency control. That is, two RFfrequency sources are used to power a plasma chamber to providesubstantially independent control of ion and electron densities.

Another approach utilizes wideband RF power sources to drive a plasmachamber. A wideband approach presents certain challenges. One challengeis coupling the power to the electrode. A second challenge is that thetransfer function of the generated waveform to the actual sheath voltagefor a desired IEDF must be formulated for a wide-process space tosupport material surface interaction. In one responsive approach in aninductively coupled plasma system, controlling power applied to a sourceelectrode controls the plasma density while controlling power applied tothe bias electrode modulates ions to control the IEDF to provide etchrate control. By using source electrode and bias electrode control, theetch rate is controlled via the ion density and energy.

As integrated device fabrication continues to evolve, so do the powerrequirements for controlling the plasma for device fabric fabrication.For example, for memory device fabrication, the requirements for biaspower continue to increase. Increased power generates higher energeticions for faster surface interaction, thereby increasing the etch rate.Increased bias power is sometimes accompanied by, in RF systems, a lowerbias frequency requirement along with an increase in the number of biaspower sources coupled to the plasma sheath created in the plasmachamber. The increased power at a lower bias frequency and the increasednumber of bias power sources results in intermodulation distortion (IMD)emissions from a sheath modulation. The IMD emissions can significantlyreduce power delivered by the source where plasma generation occurs.U.S. patent application Ser. No. 13/834,786, filed Mar. 15, 2013 andentitled Pulse Synchronization by Monitoring Power in Another FrequencyBand, assigned to the assignee of the present application andincorporated by reference herein, describes a method of pulsesynchronization by monitoring power in another frequency band. In thereferenced U.S. patent application, the pulsing of a second RF generatoris controlled in accordance with detecting at the second RF generatorthe pulsing of a first RF generator, thereby synchronizing pulsingbetween the two RF generators.

FIG. 1 depicts a RF generator or power supply system 10. Power supplysystem 10 includes a pair of radio frequency (RF) generators or powersupplies 12 a, 12 b, matching networks 18 a, 18 b, and load 32, such asa non-linear load or plasma chamber. In various embodiments, RFgenerator 12 a is referred to as a source RF generator or power supply,and matching network 18 a is referred to as a source matching network.Also in various embodiments, RF generator 12 b is referred to as a biasRF generator or power supply, and matching network 18 b is referred toas a bias matching network.

Source RF generator 12 a receives a control signal 30 from matchingnetwork 18 b generator 12 b or a control signal 30′ from bias RFgenerator 12 b. As will be explained in greater detail, control signal30 or 30′ represents an input signal to power supply 12 a that indicatesone or more operating characteristics or parameters of bias RF generator12 b. In various embodiments, a synchronization detector 34 senses theRF signal output from matching network 18 b to load 32 and outputs asynchronization or trigger signal 30 to power supply 12 a. In variousembodiments, a synchronization or trigger signal 30′ may be output frompower supply 12 b to power supply 12 a, rather than trigger signal 30. Adifference between trigger or synchronization signals 30, 30′ is theeffect of matching network 18 b, which can change the phase between theinput and output signals to matching network 18 b. Signals 30, 30′include information about the operation of bias RF generator 12 b thatenables predictive responsiveness to address periodic fluctuations inthe impedance of plasma chamber 32 caused by the bias generator 12 b.When control signals 30 or 30′ are absent, RF generators 12 a, 12 boperate autonomously.

RF generators 12 a, 12 b include respective RF power sources oramplifiers 14 a, 14 b, RF sensors 16 a, 16 b, and processors,controllers, or control modules 20 a, 20 b. RF power sources 14 a, 14 bgenerate respective RF power signals 22 a, 22 b output to respectivesensors 16 a, 16 b. Sensors 16 a, 16 b receive the output of RF powersources 14 a, 14 b and generate respective RF power signals or RF powersignals f₁ and f₂. Sensors 16 a, 16 b also output signals that vary inaccordance with various parameters sensed from load 32. While sensors 16a, 16 b, are shown within respective RF generators 12 a, 12 b, RFsensors 16 a, 16 b can be located externally to the RF power generators12 a, 12 b. Such external sensing can occur at the output of the RFgenerator, at the input of an impedance matching device located betweenthe RF generator and the plasma chamber, or between the output of theimpedance matching device (including within the impedance matchingdevice) and the plasma chamber.

Sensors 16 a, 16 b detect operating parameters of plasma chamber 32 andoutput signals X and Y. Sensors 16 a, 16 b may include voltage, current,and/or directional coupler sensors. Sensors 16 a, 16 b may detect (i)voltage V and current I and/or (ii) forward power P_(FWD) output fromrespective power amplifiers 14 a, 14 b and/or RF generators 12 a, 12 band reverse or reflected power P_(REV) received from respective matchingnetwork 18 a, 18 b or load 32 connected to respective sensors 16 a, 16b. The voltage V, current I, forward power P_(FWD), and reverse powerP_(REV) may be scaled and/or filtered versions of the actual voltage,current, forward power, and reverse power associated with the respectivepower sources 14 a, 14 b. Sensors 16 a, 16 b may be analog and/ordigital sensors. In a digital implementation, the sensors 16 a, 16 b mayinclude analog-to-digital (A/D) converters and signal samplingcomponents with corresponding sampling rates. Signals X and Y canrepresent any of the voltage V and current I or forward (or source)power P_(FWD) and reverse (or reflected) power P_(REV).

Sensors 16 a, 16 b generate sensor signals X, Y, which are received byrespective controllers or power control modules 20 a, 20 b. Powercontrol modules 20 a, 20 b process the respective X, Y signals 24 a, 26a and 24 b, 26 b and generate one or a plurality of feedback controlsignals 28 a, 28 b to respective power sources 14 a, 14 b. Power sources14 a, 14 b adjust the RF power signals 22 a, 22 b based on the receivedfeedback control signal. Power control modules 20 a, 20 b may include,at least, proportional integral derivative (PID) controllers or subsetsthereof and/or direct digital synthesis (DDS) component(s) and/or any ofthe various components described below in connection with the modules.In various embodiments, power control modules 20 a, 20 b are PIDcontrollers or subsets thereof and may include functions, processes,processors, or submodules. Feedback control signals 28 a, 28 b may bedrive signals and may include DC offset or rail voltage, voltage orcurrent magnitude, frequency, and phase components. In variousembodiments, feedback control signals 28 a, 28 b can be used as inputsto one or multiple control loops. In various embodiments, the multiplecontrol loops can include a proportional-integral-derivative (PID)control loop for RF drive, and for rail voltage. In various embodiments,feedback control signals 28 a, 28 b can be used in a Multiple InputMultiple Output (MIMO) control scheme. An example of a MIMO controlscheme can be found with reference to U.S. application Ser. No.15/974,947, filed May 9, 2018, entitled Pulsed Bidirectional RadioFrequency Source/Load and assigned to the assignee of the presentapplication, and incorporated by reference herein.

In various embodiments, power supply system 10 can include controller20′. Controller 20′ may be disposed externally to either or both of RFgenerators 12 a, 12 b and may be referred to as external or commoncontroller 20′. In various embodiments, controller 20′ may implement oneor a plurality of functions, processes, or algorithms described hereinwith respect to one or both of controllers 20 a, 20 b. Accordingly,controller 20′ communicates with respective RF generators 12 a, 12 b viaa pair of respective links 31, 33 which enable exchange of data andcontrol signals, as appropriate, between controller 20′ and RFgenerators 12 a, 12 b. For the various embodiments, controllers 20 a, 20b, 20′ can distributively and cooperatively provide analysis and controlalong with RF generators 12 a, 12 b. In various other embodiments,controller 20′ can provide control of RF generators 12 a, 12 b,eliminating the need for the respective local controllers 20 a, 20 b.

In various embodiments, RF power source 14 a, sensor 16 a, controller 20a, and match network 18 a can be referred to as source RF power source14 a, source sensor 16 a, source controller 20 a, and source matchingnetwork 18 a. Similarly in various embodiments, RF power source 14 b,sensor 16 b, controller 20 b, and match network 18 b can be referred toas bias RF power source 14 b, bias sensor 16 b, bias controller 20 b,and bias matching network 18 b. In various embodiments and as describedabove, the source term refers to the RF generator that generates theplasma, and the bias term refers to the RF generator that tunes theplasma Ion Energy Distribution Function (IEDF) relative to the bias RFpower supply. In various embodiments, the source and bias RF powersupplies operate at different frequencies. In various embodiments, thesource RF power supply operates at a higher frequency than the bias RFpower supply.

In various embodiments, source controller 20 a adjusts the frequency ofRF signal f₁ to compensate for impedance fluctuations, includingimpedance fluctuations resulting from the application of RF signal f₂ toplasma chamber 32. In various embodiments, RF signal f₂ is a frequencylower than the frequency of RF signal f₁. The lower frequency causesperiodic impedance fluctuations in plasma chamber 32, which appear asreflected intermodulation distortion (IMD). In various embodiments, andas will be described in greater detail herein, adjusting the timing ofapplication of RF signal f₁, the source signal, in relation to RF signalf₂, the bias signal, enables an increase of delivered power atpredetermined, desired portions of the RF signal f₂. The adjusting thepower output of RF signal f₁ can include synchronizing power delivery off₁ relative to f₂, increasing power at predetermined portions of RFsignal f₂, decreasing or cutting off power of source RF signal f₁ atpredetermined portions of bias RF signal f₂, or a combination thereof.In various embodiments, using the periodic nature of both RF signals f₁and f₂, frequency offsets or hops can be added to RF signal f₁ tocompensate for anticipated impedance fluctuations introduced by RFsignal f₂. The power timing, power amplitude, and frequency offsets canbe predetermined and stored in one or multiple lookup tables, or may bedetermined dynamically.

FIG. 2 depicts a RF power delivery system 40. Power delivery system 40can represent the operation of one or either of power supplies 12 a, 12b of FIG. 1. Power delivery system 40 includes a RF generator 12 thatfurther includes a power controller 42, power amplifier 44, and sensor16. RF generator 12 also includes a scalar module 46, which receivesoutput signals X, Y from sensor 16. Scalar module 46 generates afeedback signal representative of the forward power y_(fwd) ^(P) inputto summer 48. Summer 48 also receives a power setpoint and determines adifference or error e_(fb) input to power controller 42. It will beunderstood by one skilled in the art that RF power source 14 of FIG. 1may include one or both of power controller 42 and power amplifier 44.Likewise, it will be understood that power controller 42 can also bedistributed across either or both of RF power source 14 and controller20. Further, implementation of scaling module 46 and summer 48 can alsobe distributed across one or both of RF power source 14 and controller20. RF power delivery system 40 typically operates by measuring eithervoltage and current or forward power and reverse power output as signalsX, Y, which are scaled by scaling module 46 to produce a calibratedfeedback power measurement y_(fwd) ^(P) input to summer 48. Thecalibrated feedback power measurement is compared to a desired powersetpoint, and an error signal is used to drive one or more controlactuation signals to maintain the desired output power.

In a typical RF power delivery system, matching network 18 is adjustedto achieve maximum power delivery to load 32 via tunable mechanicalcomponents. The maximum power delivery is indicative of a minimumreflected power. Because the response times of the electro-mechanicaltuning elements in matching network 18 are comparatively slow,adjustment of matching network 18 may take a relatively extended periodto complete the power adjustment. In order to improve impedancematching, the RF frequency output by power amplifier 44 may also beadjusted. Frequency-based tuning improves performance and providesresponsiveness several orders of magnitude faster than adjustment ofelectro-mechanical components of matching network 18.

When employing frequency-based impedance matching, it is desirable tofind an optimal frequency that provides minimum reflected power. Theminimum reflected power may be indicated through a minimum magnitude ofthe measured complex reflection coefficient gamma, |Γ|. There are anumber of existing methods for adjusting the RF frequency. These methodsinclude search-based methods and control-based methods. Control-basedmethods typically require a more complete understanding of the processthan search-based methods. That is, control-based methods may rely on amodel or a transfer function.

In one search-based method, a low-level secondary signal is superimposedon the RF signal to sweep over the entire band. Measurements at thefrequency of the secondary signal can be used to determine a frequencyat which reflected power is minimized. The search-based methods can beviewed as an optimization challenge, where gradient descent, or othersearch-based methods yield a maximum or minimum cost in a set ofoptimized constraints or electrical parameters. Search-based methods,however, tend to require extended periods to converge compared tocontrol-based approaches. Further, search-based methods require abalance between a time required to arrive at a solution with assuringconvergence to a solution. For example, larger step sizes in theinjected, low-level secondary signal increase the speed of the searchalgorithm, but at the cost of possibly not converging to a stablesolution. A criteria can be used to determine when to terminate thesearch once the measured performance falls within a certain threshold.This ensures convergence and prevents instability in the steady-statesolution. Further, the selection of parameters that guide the search canbe a challenge to ensuring desirable performance, particularly sincemany of the performance criteria require opposing constraints, such asfinding the solution quickly, but also ensuring that a stable solutionis always found.

Control-based methods for auto-frequency tuning include direct frequencytuning or reference vector tuning in which a reference vector divides aSmith chart into regions where frequency needs to increase or decrease.Frequency step size is determined by the angle between the presentreflection coefficient F and a reference vector. In direct frequencytuning, the phase difference between two measured process signals, suchas voltage, current, forward power, or reverse power, is minimized toachieve the optimal frequency tuning setpoint. Put in another way, thedirect frequency tuning approach is intended to minimize the imaginarypart of the complex reflection coefficient, Γ. In general, control-basedauto-frequency tuning approaches experience reduced accuracy whenprocess dynamics are not modeled with sufficient accuracy. Manycontrol-based methods attempt to simplify process dynamics into aclosed-form model, such as a transfer function, that does notsufficiently describe major aspects of the process behavior. The modelsare then used to develop and tune a control algorithm to calculate therequired actuator updates.

Control-based methods provide an inherent tradeoff in the complexity ofthe process models and the controller implementation. If the models incontroller implementation are over-simplified, the control design willnot incorporate sufficient process behavior, and the performance of thetuner may lack sufficient accuracy. On the other hand, models that areoverly complex may result in a tuner that does not sufficiently react toactual process dynamics relative to the model. Further, since impedanceresponse with frequency can be highly non-linear, yet be stronglycoupled, the tradeoff between the impedance response and frequency canprove challenging. In various control-based scenarios, onlinecalibration can be used to learn key aspects of the model and to adjustappropriately as the process dynamics change with time. Suchcalibrations can be time consuming, require storage for measuredparameters, and can introduce performance degradation if notrecalibrated with sufficient regularity.

FIG. 3 depicts a Smith chart plot of a complex reflection coefficient Facross a range of input RF frequency operating conditions. By way ofnon-limiting example, the Smith chart of FIG. 3 was developed using a400 kHz generator attached to a matching network and a fixed load. Theoperating frequency of the generator was cycled between 340 kHz and 440kHz, while the load impedance at the RF generator was measured. As isknown by those skilled in the art, the most desirable operatingcondition, indicative of a complete match between RF generator 12 andload 32, occurs at the center of the Smith chart 54. As is known, thecenter of the Smith chart corresponds to a zero imaginary component ofthe reflection coefficient. Thus, considering the range of frequenciesresulting in the impedance variation between the reflection coefficientplotted in FIG. 3 between points 56 and 58, the center of the Smithchart at point 54 represents an ideal match condition.

FIG. 4 depicts a Smith chart plot of a reflection coefficient in which acrossing of the imaginary axis is not necessarily an optimal tune point.In FIG. 4, the reflection coefficient translates along a curve from afirst end position 60 to a second end position 62. The reflectioncoefficient crosses the imaginary axis at position 64. Although position64 indicates a zero crossing of the imaginary axis, one skilled in theart will recognize that position 62 is closer to the center of the Smithchart and, thus, indicates a lesser magnitude of the reflectioncoefficient than position 64. Thus, position 64 provides a lowerreflected power than the zero crossing occurring at position 64. Forexample, position 64 yields approximately 90% delivered power, whileposition 62 yields approximately 98% delivered power, which correspondsto respective magnitudes of the reflection coefficient of 0.3201 and0.1532.

FIG. 5 depicts a Smith chart showing a plot of the reflectioncoefficient between a first end position 66 to a second end position 68.Position 68 indicates a first zero crossing of the imaginary axis, and asecond position 70 indicates a second zero crossing of the imaginaryaxis. As can be seen in FIG. 5, although position 70 represents zerocrossing the imaginary axis, zero crossing 68 is closer to the center ofthe Smith chart. For example, the delivered power at position 70 isapproximately 55%, while the delivered power at position 68 isapproximately 100%, corresponding to respective magnitudes of thereflection coefficient of 0.6726 and 0.0058. Thus, depending upon howthe frequency changes, whether from position 66 to 68 or position 68 to66, it is possible that an auto frequency tuning implementation directedto minimizing the imaginary component of the reflection coefficientcould select a less desirable match condition by choosing the less idealcrossing of the imaginary axis on the Smith chart.

In various configurations, it is possible that a less desirable matchposition, whether position 64 of FIG. 4 or position 70 of FIG. 5, couldbe selected based upon the arbitrary starting point for the tuningalgorithm. Based upon the arbitrary starting point, it is possible thatthe auto tuning controller will approach the closer, less desirable zerocrossing of the imaginary axis. Some auto frequency tuning algorithmsaddress possible selection of less desirable frequencies, such as atposition 64 of FIG. 4 or position 70 of FIG. 5 by implementing acalibration step. However, the calibration step may be required to beperformed for each major operating condition of a plasma fabricationprocess.

The present disclosure is directed to an extremum seeking control (ESC)based approach for performing auto frequency tuning of a RF powerdelivery system. The ESC approach minimizes reflected power withoutrequiring extensive knowledge of the process. The ESC approach describedin the various embodiments herein implements a dynamic adjustmentmechanism to auto tune the frequency along a direction of a gradient ofa cost function without requiring an explicit model of the system orprocess. As described herein, a cost function J can be generallyreferred to as a functional equation that maps a set of points to asingle scalar value. It is generally desirable to minimize or maximize acost function J. The scalar value that results from solving a costfunction J can be referred to as a cost.

In accordance with the various embodiments described herein, FIG. 6depicts a schematic view of a cost function J 80 implemented as a plotof a quadratic function having a single maximum 86. As will be describedwith respect to FIGS. 6-8, cost function J 80 includes a first positionA 82 and a second position B 84, each being on different sides ofmaximum 86. Accordingly, all points to the left of maximum 86 have apositive slope, and all points to the right of maximum 86 have anegative slope. Accordingly, at operating point A 82, moving theactuator u to the right (higher) results in an increased output responsevalue, while moving the actuator u to the left (lower) results in adecreased output response value. Conversely, at operating point B 84,moving the actuator u to the right (higher) results in a smaller outputresponse, while moving the actuator u to the left (lower) results in anincreased output response value. The difference in the relationshipbetween the directionality of the input and output response can be usedto seek the extremum (maximum). It will be understood by one skilled inthe art, that similar relationships exist in connection with a quadraticcost function J having a minimum, such as where cost function J 80 ofFIG. 6 is rotated 180 degrees.

FIG. 7 depicts a block diagram 90 having an input varying sinusoidallyin accordance with a function sin(ωt). Block diagram 90 of FIG. 7includes process dynamics 92, cost function module 94, filter 96, suchas a high pass filter, and mixer 98. The input sin(ωt), an excitation orperturbation signal, is input to process dynamics 92. Process dynamics92 represents a system response to the sin(ωt) input and outputs a valueu input to cost function 94. Cost function 94 generates an output Jinput to filter 96. Filter 96 is implemented as a high pass filter,which generates an output Filter_(out) input to mixer 98. Mixer 98 alsoreceives the input sin(ωt) the output of mixer 98 results in a productof sin(ωt) and Filter_(out).

FIG. 8 depicts the responses at respective points A and B, such aspoints 82, 84 of FIG. 6, in response to the input signal sin(ωt) at FIG.7. With respect to position A 82, the Filter_(out) signal is in phasewith the sin(ωt) signal so that the product sin(ωt)×Filter_(out) is inphase, resulting in a product which is always positive. Thus, as shownat FIGS. 6-8, whenever actuator u is to the left of maximum 86, anyadjustment to u results in a response that is in phase with theadjustment to the actuator. That is, an increase in actuator u resultsin an increase in cost function J, and a decrease in actuator u resultsin a decrease in cost function J.

At position B 84, the Filter_(out) is out of phase with the inputsin(ωt), resulting in a product sin(ωt)×Filter_(out) which is negative.Thus, at position B 84, to the right of maximum 86 of FIG. 6, any changein cost function J is out of phase with actuator u. In other words, anincrease in actuator u results in a decrease in the cost function J,while a decrease in the actuator u results in an increase in the costfunction J.

Put another way, the product output by mixer 98 results in either an allpositive or an all negative signal depending on whether cost function Jincreases or decreases in response to changes in the input perturbationsignal sin(ωt). If the positive half cycle of the input perturbationsignal causes the output to increase and the negative half cycle causesthe output to decrease, then an all positive output will be achievedfrom the output of filter 96 and mixing process 98. Similarly, if thenegative half cycle of the input perturbation signal sin(ωt) causes theoutput to increase and the positive half cycle causes the output todecrease, then an all negative output will be achieved after filter 96and mixer 98.

In various embodiments, by sending the post mixer signal through anintegrator, the control system can achieve a result that willautomatically move in the direction it pushes the output cost function Jtowards the maximum value. The amplitude of the signal will vary withthe slope of the response curve so that as the actuator nears theoptimum value, which corresponds to the minimum or maximum of a costfunction curve, the slope of the response approaches zero. Further, ifthe integrated signal becomes the input actuation value for the processto be controlled, the controller can automatically steer towards themaximum value of the cost function without prior knowledge of theprocess or cost function.

FIG. 9 depicts a power delivery system 100 including a power controlsystem 110 providing output to a match network 112, which in turnprovides output to a load 114, such as non-linear load or plasmachamber. Power control system 110 includes a power controller 116, apower amplifier 118, and a sensor 120. Sensor 120 may be implemented asone of a voltage/current sensor (VI sensor) or a directional coupler, asdescribed above. Power controller 116 outputs an actuation signal u_(fb)^(p) input to power amplifier 118. The u_(fb) ^(p) signal represents apower control signal responsive to a feedback signal, as will bedescribed herein. Power amplifier 118 generates an output RF signal tosensor 120 as commanded by u_(fb) ^(p). Sensor 120 outputs the RF signalto match network 112 for application to load 114. Sensor 120 outputsfeedback signals X, Y to block 122. In various embodiments, block 122can be a scaling or calibration module that scales X and Y to outputpredetermined electrical parameters. Block 122 outputs a forward powervalue y_(fwd) ^(P) to summer 124. Summer 124 also receives a powersetpoint input, and determines a difference between the power setpointinput and the forward power value y_(fwd) ^(P) error. Error e_(fb) isinput to power controller 116. The error signal e_(fb) input to powercontroller 116 determines a desired adjustment to u_(fb) ^(P) made bypower controller 116 to power amplifier 118.

Block 122 also outputs the magnitude of the reflection coefficient |Γ|.The magnitude of the reflection coefficient |Γ| is input to block 126which implements a high pass filter with a transfer function to removeany DC bias D_(filt)(z). The filtered magnitude of |Γ| is input to amixer 123. Mixer 123 also receives a perturbation signal u_(e) ^(p). Asshown at FIG. 9, perturbation signal u_(esc) ^(P) is represented as asinusoidal signal sin(ω_(pert)t) generated by signal source 129, has asinusoidal frequency ω_(pert), and is analogous to the perturbationsignal described above with respect to FIGS. 6-8. Mixer 123 thus mixesthe perturbation signal u_(esc) ^(p) and the measured magnitude of thecomplex coefficient |Γ|. The output of mixer 123 is analogous to theproduct defined with respect to FIGS. 7 and 8 and represents a scaledpositive or negative square of the perturbation signal u_(esc) ^(p). Theoutput from mixer 123 is input to an integrator D_(esc)(z) 125 whichgenerates a frequency control or frequency feedback signal u_(esc) ^(f)input to signal combiner or adder 127. Thus, the feedback signal u_(esc)^(f) is combined with the perturbation signal u_(esc) ^(P) to generate afeedback component or a frequency control signal u_(esc) ^(t). Thefeedback component or frequency control signal u_(esc) ^(f) may bedescribed below in Equation (1):u _(esc) ^(t) =u _(esc) ^(f) +u _(esc) ^(p)  (1)where:

u_(esc) ^(f) is a frequency tuning signal component to adjust thefrequency to achieve auto-frequency tuning of the power delivery system,

u_(esc) ^(p) is a perturbation signal component, which is theperturbation signal for the next iteration of the control loop.

The u^(t) _(esc) signal may be a complete frequency control signal(center frequency and AFT offset) or only an automatic frequency tuning(AFT) offset from the center frequency. In various non-limitingembodiments, if the center frequency of the system is 13.56 MHz, theu^(t) _(esc) signal may represent an offset from 13.56 MHz to enableautomatic frequency tuning or may be a desired output frequency, 13.58MHz, for example.According to various embodiments, various portions of the block diagramof FIG. 9 can be considered to cooperate to define a frequencycontroller, or such components can include all or part of elements 123,125, 127, and 129.

In various embodiments, two perturbation signals, one input to combiner127 and one input to mixer 122, may be used, rather than the oneperturbation signal output by signal source 129. A second perturbationsignal u_(esc) ^(p1) is output by a second signal source 129′ thatoutputs a signal sin (ω_(pert)′t). In various other embodiments, mixer127 may output a match control signal u_(esc) ^(t)′ generated similarlyto equation (1) above to control operation of match network 112. Invarious other embodiments, u_(esc) ^(t)′ can control one of an impedancetuning actuator, such as a reactive component embodied as a capacitor orinductor to vary a reactance of match network 112.

Further referring to FIG. 9, the resulting feedback signal from sensor120, in various embodiments, the magnitude of complex coefficient gamma|Γ|, is applied to a high-pass filter 126 that imposes a transferfunction D_(filt)(z) to remove any DC bias. The result is mixed with theperturbation signal u_(esc) ^(P)=sin(ω_(pert)t) at mixer 123. The outputfrom mixer 123 is input to block 125, which implements a transferfunction D_(esc)(z) to generate the feedback component u_(esc) ^(f) ofthe overall frequency actuator signal. The transfer function D_(esc)(z)that generates the feedback component u_(esc) ^(f) may be characterizedas in Equation (2) below:

$\begin{matrix}{{D_{esc}(z)} = \frac{K_{int}}{\left( {z - 1} \right)}} & (2)\end{matrix}$where:

K_(int) is an integration constant, and

z indicates the z-transform variable.

The integration performed by Equation (2) produces an actuator valuethat will shift up or down depending on which direction moves the outputtowards its maximum. Other formulations of the D_(esc)(z) are possibleto achieve additional shaping of the actuator and system response.

In various embodiments, the perturbation signal can include a variableamplitude that can be tuned to achieve robust ESC response. To maximizethe response time when a controller is farther from the solution, whilealso minimizing the steady state perturbation injected into the process,various embodiments can employ an adaptive adjustment of theperturbation amplitude. One example adjustment of perturbation amplitudewould be a second order function of the magnitude of gamma |Γ| asdescribed below at Equation (3):u _(esc) ^(p)=[aΓ _(mag) ² +bΓ _(mag) +c] sin(ωt)  (3)where:

Γ_(mag) is the magnitude of the reflection coefficient, as describedabove,

ω is the frequency, as described above, and

a, b, and c are predetermined coefficients.

Through the appropriate selection of tuning parameters a, b, c theamplitude of the sinusoidal perturbation can be weighed by the distancefrom the correct solution, resulting in the application of higherperturbation signals when farther from the solution and smallerperturbation signals when nearer to the solution. Other adaptive optionsfor the perturbation signal include amplitude scaling, including scalingthe threshold and perturbation amplitudes based on the desired |Γ|criteria. In various embodiments, if the measured performance is withina certain acceptable level, a decreased probe signal can be used. On theother hand, for larger errors, a larger probe signal would be used.

FIG. 10 is a plot of the magnitude of the reflection coefficient |Γ|versus frequency according to various embodiments of FIG. 9. In thevarious embodiments, a set of frequency sweep data was obtained with a60 MHz generator. Sweeps were conducted at different match capacitorsettings on the match network to provide a variety of representativeoperating conditions. The magnitude of |Γ| versus frequency for fivematch capacitor sweeps are indicated in FIG. 10. These data were used togenerate a simulation model representing the cost function J for variousmatch capacitor settings. Given a frequency actuation from the ESCtuner, the simulation model predicted the next |Γ| value. As can be seenin FIG. 9, each match capacitor setting resulted in a slightly differentminimum magnitude of |Γ|, with three match capacitor settings providingthe minimum at 58 MHz and two taps providing a minimum at about 57.5MHz.

The data of FIG. 10 was used to test the ESC method in a simulation.FIG. 11 depicts frequency with respect to time and is directed to astressful scenario in which the match capacitor position (the magnitudeof |Γ| versus the frequency data position) were repeatedly alternatedbetween two positions. As can be seen in FIG. 12, based on the frequencysweep data in FIG. 10, the optimal |Γ| values obtained were 0.427 and0.290 for the two match capacitor positions. As indicated in FIG. 12,the tuner was able to successfully find the optimal values. In FIG. 11,positions 130, 132 on the waveform indicate changes in the matchcapacitor position, and FIG. 12 indicates the resulting change in themagnitude of |Γ| in response to the change in match capacitor positions.For example, positions along the waveform of FIG. 12 134 represent thechange in the match capacitor position occurring at 130 of FIG. 11, andthe positions 136 of FIG. 12 represent the change in the match capacitorposition at 132 of FIG. 11. Thus, FIGS. 11 and 12 demonstrate that theESC tuner achieves minimum possible reflected power at a given operatingcondition, such as the match capacitor setting indicated by FIG. 10.

FIGS. 13-15 represent operation of the ESC tuner under differentoperating conditions according to various embodiments. In the powerdelivery system characterized by FIGS. 13-15, a 400 kHz generator isconnected to an adjustable matching network and a static load. Theparameters of the adjustable matching network were adjusted to create amismatched load for the generator, indicating a challenging distortiontrajectory, such as indicated at FIG. 13. As shown in the Smith chart ofFIG. 13, the plot of the magnitude of the reflection coefficient |Γ|includes a first end stop 140, a zero crossing 142, a position nearestthe center of the Smith chart 144, and a second end stop 146. Thedelivered power calculations for positions 142, 144, and 146 are 94.8%,99.5%, and 96.5%, respectively. Thus, an optimal solution would beposition 144, nearest the center of the Smith chart of FIG. 13.

FIG. 14 is a plot of the magnitude of |Γ| versus frequency plotted on awaveform 150. In accordance with FIG. 13, the frequency that results inposition 144 in FIG. 13 should be the frequency selected by thefrequency tuner implementing an ESC control approach, which appears atposition 152 on waveform 150. The frequency is thus approximately 355kHz at position 152. In a simulation, the prototype ESC tuner selectedoptimal solution at a frequency of 356 kHz, regardless of the startingfrequency in FIG. 13, as can be seen from waveform 156 of FIG. 15 atwhich the tuning trajectory for the frequency actuator for a startingfrequency of 400 kHz is shown to reach steady state in region 158 at 355kHz.

FIG. 16 shows a control module 170. Control module 170 incorporatesvarious components of FIGS. 1, 7, and 9. Control module 170 may includeamplitude control module 172, frequency control module 174, and matchnetwork control module 176. Control module 170 may also includeperturbation module 178, frequency tuning module 180, and costdetermination module 182. In various embodiments, control module 170includes one or a plurality of processors that execute code associatedwith the modules 172, 174, 176, 178, 180, and 182. Operation of themodules 172, 174, 176, 178, 180, and 182 is described below with respectto the method of FIGS. 17-22.

For further defined structure of controllers 20 a, 20 b, and 20′ ofFIGS. 1, 7, and 9, see the below provided flow charts of FIGS. 17-22 andthe below provided definition for the term “module”. The systemsdisclosed herein may be operated using numerous methods, example,various control system method of which are illustrated in FIGS. 17-22.Although the following operations are primarily described with respectto the implementations of FIGS. 1 and 9, the operations may be easilymodified to apply to other implementations of the present disclosure.The operations may be iteratively performed. Although the followingoperations are shown and primarily described as being performedsequentially, one or more of the following operations may be performedwhile one or more of the other operations are being performed.

FIG. 17 a flow chart of a control system 200 for performing automaticfrequency tuning (AFT), for example, for the power delivery systems ofFIGS. 1 and 9. Control begins at block 202, where initialization occurs.Control proceeds to block 204 in which an electrical parameter ismeasured. In various embodiments, the electrical parameter can be onethat varies in accordance with the match between a power supply, such aspower supply 12 of FIG. 1 or power supply 110 of FIG. 9, and a load,such as a load 30 of FIG. 1 or load 114 of FIG. 9. For example, theelectrical parameter can be the magnitude of the reflection coefficient|Γ|. In various embodiments, the electrical parameter can be one or moreof forward power, reverse power, voltage, current, frequency, or otherelectrical parameters. Control proceeds to block 206 in which parametercontrol signal is combined with the perturbation signal, as describedabove. The perturbation signal perturbs at least one electricalparameter controlled by the control signal.

At block 208, the electrical parameter is mixed with the perturbationsignal, such as may occur at mixer 123 of FIG. 9. Blocks 210, 212, and214 implement at least part of the function of block 125 of FIG. 9 anddepict a representation of integration affects adjustment of the atleast one parameter controlled by the parameter control signal. Invarious embodiments, the control signal may be one of phase, frequency,amplitude, match network settings, or other electrical characteristics.The measured parameter may be one of a quantity that varies with respectto the control signal, such as power, voltage, current, a reflectioncoefficient, or similar parameters. At block 210, it is determinedwhether the measured parameter, using an ESC approach, is in phase orout of phase with the perturbation signal. If the mixed signal is inphase with the perturbation signal, control proceeds to block 212. Atblock 212, the at least one parameter control signal is increasedtowards a maximum (or decreased towards a minimum). Control nextproceeds to block 216, which returns the cost and the value of theparameter control signal, such as frequency. Returning to block 210, ifthe measured parameter, using an ESC approach, is out of phase with theperturbation signal, control proceeds to block 214. At block 214, the atleast one parameter control signal is decreased toward a minimum (orincreased towards a maximum). Control next proceeds to block 216, whichreturns the cost and the value of the parameter, such as frequency.Example cost adjustment approaches can be seen in FIGS. 18-22.

FIG. 18 depicts a flow chart 230 for monitoring and updating the costvalue if the cost value exceeds a predetermined threshold while in asteady state tune mode, such as automatic frequency tuning. If the costvalue exceeds the predetermined threshold, a learning cycle is executed.If the cost value does not exceed the predetermined threshold, the ESCalgorithm continues, according to FIG. 17, for example, to maintain aposition near the minimum cost value.

Control begins at start block 232 and proceeds to block 234. At block234, the automatic frequency tuning frequency is updated, as describedabove with respect to FIG. 17. Control then proceeds to block 236 whichdetermines whether a minimum cost has been reached. Achievement of astable minimum cost value can be determined using a variety of methods.In one embodiment, the cost value is monitored to see if consecutivesamples are within a pre-determined difference or delta. If so, thesteady-state minimum cost has been reached. In an alternate embodiment,the output of the ESC tuner is monitored. If consecutive samples arewithin some pre-determined difference or delta, the steady-state minimumcost has been reached. If a minimum cost has not been reached, controlreturns to block 234. If a minimum cost has been reached, controlproceeds to block 238. At block 238, a present cost value is compared toa predetermined cost threshold [t. If the cost value is less than thepredetermined cost threshold C_(t), control returns to block 234. If thecost value is greater than the predetermined cost threshold C_(t),control proceeds to block 240 which initiates a learning cycle, as willbe described in connection with FIGS. 19-22.

FIG. 19 depicts a flow diagram or chart 250 for adjusting frequency toachieve a minimum value of the cost function, even if a non-ideal localminimum exists in the reflection coefficient versus frequency curve. Inthe descriptions of the various flow charts throughout the specificationit will be understood that a similar approach can be used to adjustfrequency, parameter control signal, phase, amplitude, or some otherelectrical parameter to find a maximum value of a cost function, forinstance, of the measured electrical parameter delivered power. In flowdiagram or chart 250, incremental frequency changes are initiated ateither the frequency minimum f_(min) or frequency maximum f_(max) of apredetermined tune frequency range in order to search for the localminimum value of the cost function. If the minimum value of the costfunction is considered sufficient at the end of a first iteration, theprocess completes. If the minimum value of the cost function isdetermined not to be sufficient, a second iteration of incrementalfrequency changes in a direction opposite the first iteration startsfrom the other of the frequency minimum f_(min) or frequency maximumf_(max) of the predetermined frequency. The outcome is either adjustingfrequency to achieve an acceptable operating condition (minimum costvalue) or declaring a fault.

Flow diagram or chart 250 commences at block 240 a, such as block 240from FIG. 18, and proceeds to block 254 where the frequency is set to aminimum f_(min) of the frequency tune range. Control proceeds to block256 where the automatic frequency tuning is updated as described abovewith respect to FIG. 17. Block 258 determines if the minimum cost valuehas been reached. If the minimum cost value has not been reached,control returns to block 256, and the frequency of the frequency tuneris again incremented. Returning to block 258, if the minimum cost valueC_(min) has been reached, control proceeds to block 260, where it isdetermined if the minimum cost C_(min) is less than a predetermined costthreshold C_(t). If the minimum cost C_(min) is less than the costthreshold C_(t), control proceeds to block 262 where the control systementers the steady-state mode.

Returning to block 260, if the minimum cost C_(min) is greater than thecost threshold C_(t), control proceeds to block 266 at which the minimumcost C_(min) is recorded as C₁ and the present auto tune frequency f₁yielding C₁ is recorded. Control proceeds to block 270 where the tunefrequency is set to the maximum f_(max) of the tune frequency range. Atblock 272, the automatic frequency tuning is updated as described abovewith respect to FIG. 17. Control then proceeds to block 272 whichdetermines if the minimum cost value is reached. If the minimum costvalue has not been reached, control returns to block 272, and thefrequency of the frequency tuner is again incremented.

Returning to block 274, if the minimum cost value is reached, controlproceeds to block 276, at which the tune frequency f₂ and the cost C₂associated with frequency f₂ are recorded. At block 278, if cost C₂ isless than the cost threshold C_(t), control proceeds to block 262 wherethe control system enters the steady-state mode. If cost C₂ is greaterthan C_(t), control proceeds to block 280, a fault is declared since nocost C₁ or C₂ is less than the cost threshold C_(t). From either block262 or 280 control proceeds to end block 268.

FIG. 20 depicts a flow diagram or chart 290 for determining a minimum ofthe cost function. In flow diagram or chart 290, an initial condition f₀is set, and the frequency is adjusted to achieve a nearest minimum valueof the cost function. If the minimum value of the cost function isconsidered sufficient at the end of a first iteration, the processcompletes. If the minimum value of the cost function is determined notto be sufficient, a second iteration starting at the furthest frequencyextreme in the frequency tune range is initiated to determine a secondminimum cost value.

Flow diagram or chart 290 commences at block 240 b and proceeds to block294 where the frequency is set to a start frequency f₀. Control proceedsto block 296 which updates the automatic frequency tuner frequency asdescribed above with respect to FIG. 17. Block 298 determines if theminimum cost value has been reached. If the minimum cost value has notbeen reached, control returns to block 296, and the frequency of thefrequency tuner is again adjusted as described above with respect toFIG. 17. Returning to block 298, if the minimum cost value has beenreached, control proceeds to block 300, where it is determined if theminimum cost C_(min) is less than the cost threshold C_(t). If theminimum cost C_(min) is less than the cost threshold C_(t), controlproceeds to block 302 where the control system enters the steady-statemodel.

Returning to block 300, if the minimum cost C_(min) is greater than thecost threshold C_(t), control proceeds to block 306 at which the minimumcost C_(min) is recorded as C₁ and the autotune frequency f₁ yielding C₁are recorded. At block 308, if f₁ is less than the middle of thefrequency tuner range f_(mid), control proceeds to block 310, where thetune frequency is set to the maximum of the tune frequency range. If f₁is greater than the middle of the frequency tuner range f_(mid), controlproceeds to block 312, where the tune frequency is set to the minimum ofthe tune frequency range. From either of blocks 310 or 312, controlproceeds to block 314, where the automatic frequency tuning frequency isupdated as described above with respect to FIG. 17 towards the middlefrequency f_(mid) of the tune frequency range. Block 316 determines ifthe minimum cost value has been reached. If the minimum cost value hasnot been reached, control returns to block 314, and the frequency of thefrequency tuner is incremented towards the middle frequency of thefrequency tuning range f_(mid). Returning to block 316, if the minimumcost value is reached, control proceeds to block 318 at which theminimum cost C_(min) is recorded as C₁ and the present autotunefrequency f₂ yielding C₂ are recorded. At block 320, if cost C₂ is lessthan cost threshold C_(t), control proceeds to block 302 where thecontrol system enters the steady-state mode using the updated frequencyfrom block 314. If cost C₂ is greater than C_(t), control proceeds toblock 322, and a fault is declared. From either block 302 or 320 controlproceeds to end block 308.

FIG. 21 depicts a flow diagram or chart 330 for determining a minimumvalue of the cost function where there are two minima in the impedanceversus frequency curve. Control starts from an initial condition andproceeds to the nearest minimum of the cost function. If the minimumvalue of the cost function is considered sufficient at the end of afirst iteration towards the nearest minimum, the process completes. Ifthe minimum value of the cost function is determined not to besufficient, the process enters a minimization mode to determine the peakfrequency value. The frequency is iteratively controlled past the peakfrequency by a predetermined offset f_(delta) and initiates anotherminimization process. If the first peak is at one of the end stops ofthe frequency tuning range, the frequency changes to the opposite sideof the minimum to locate a peak in the direction of the opposite side ofthe minimum.

The process commences at block 240 c and proceeds to block 334 at whichthe cost is recorded as C₁ and the frequency f₁ yielding C₁ arerecorded. At block 336, a minimum frequency determination routine isexecuted to determine a frequency f_(min) associated with a minimum costC_(min). FIGS. 19 and 20 are non-limiting examples of approaches todetermining f_(min) and C_(min). At block 338, if the minimum costC_(min) is less than the cost threshold C_(t), a steady-state controlmode is entered at block 340, and control ends at 342. Returning toblock 338, if the minimum cost C_(min) is greater than the costthreshold C_(t), control proceeds to block 344. If f_(min) is less thanf₁, a positive direction is selected for the increment. If f_(min) isgreater than f₁, a negative direction is selected for the increment.

At block 350, the start frequency f_(start) is set to commence atf_(min) in predetermined increments f_(delta) in the directiondetermined in accordance with the determination of f_(min) and f₁ atblock 344. A block 352, a counter is set to 0, and at block 354, amaximization process is carried out to determine a frequency f_(max)associated with a local maximum cost C_(max). FIGS. 19 and 20 arenon-limiting examples of approaches to determining f_(max) and C_(max)but for determining maximums rather than minimums. At block 356, iff_(max) is at a limit of the auto frequency tuning range, controlproceeds to block 358 where the counter is incremented. At block 360, ifthe counter is 0 or 1, indicating that the frequency is near an end ofthe frequency tuning range, control proceeds to block 362, which changesthe Direction variable in order to change direction of the frequencyincrement. Control proceeds to block 364, at which the start frequencyf_(start) is set to commence at f_(min) in predetermined incrementf_(delta) in an opposite direction determined in accordance with thedetermination of f_(min) and f₁ at block 344. Control returns to block354 and then to block 356.

At block 356, if f_(max) is not at a limit of the auto frequency tuningrange, block 370 determines if f_(max) is greater than startingfrequency f_(start). If f_(max) is greater than f_(start), a positivedirection is selected for the increment. If f_(max) is less thanf_(start), a negative direction is selected for the increment. Controlproceeds to block 376, at which the start frequency f_(start) is set tocommence at f_(max) offset in a predetermined increment f_(delta) in thedirection determined at block 370. At block 378, a minimum frequencydetermination occurs to determine a frequency f_(min) associated with alocal minimum cost C_(min), as described above. If the minimum costC_(min) is less than the current cost C_(t), a steady-state control modeis entered at block 382, and the control ends at 368. Returning to block380, if the minimum cost C_(min) is greater than the current cost C_(t),control proceeds to block 366 where a fault is declared. From eitherblock 366 or block 382, control terminates at block 368.

FIG. 22 depicts a flow diagram or chart 390 for determining a minimum ofthe cost function by first initiating a course sweep of the frequencyactuator across the auto frequency tune range. The sweep progressesuntil the cost value (the reflected power or magnitude of gamma) isbelow a course tune threshold C_(coarse). Once the cost value is belowthe course tune threshold C_(coarse), an ESC fine tuning mode is carriedout to find a minimum value of the cost.

Control begins a block 240 d and progresses to block 394 were a counteris set to 0. A block 396 an ignition timeout timer is reset. At block398, the auto tune frequency f is updated by an increment of the presentauto frequency f by a predetermined f_(step) in a predetermineddirection. At block 400, if the updated frequency is a maximum orminimum value, indicating the frequency is at the end of the autofrequency tuning range, control proceeds to block 402 where the counteris incremented. Control proceeds to block 404, where it is determined ifthe count is less than a predetermined maximum allowable numberiterations. If the count is less than the maximum that indicates anumber of times the frequency may be updated, control proceeds to block408 in which the Direction is changed. Control proceeds to block 398where the frequency is updated. Returning to block 404, if the maximumallowable number of times that the frequency may be updated has beenexceeded, control proceeds to block 406 where a fault is indicated.Control then proceeds to block 424 where the process is terminated.

Returning to block 400, if the updated frequency is not the maximum orminimum frequency, control proceeds to block 410 where it is determinedif a timeout, reset at block 394, has occurred. If a timeout hasoccurred, control proceeds to block 406 where fault is declared, and theprocess terminates at block 424. If a timeout has not occurred, block142 determines whether the cost is less than the course tune thresholdC_(coarse). If the cost is greater than the course tune thresholdC_(coarse), control returns to block 398. If the cost is less than thecourse tune threshold C_(coarse), control proceeds the block 414 whichupdates the auto frequency tuner frequency as described above withrespect to FIG. 17. Control proceeds to block 416 where it is determinedif the minimum cost value has been reached. If the minimum cost valuehas not been reached control returns to block 414. If the minimum costvalue has been reached, control proceeds to block 418 where the minimumcost associated C_(min) and the associated minimum frequency f_(min) arerecorded. At block 420, if C_(min) is less than the current cost C_(t),control proceeds to block 422 in which a steady-state tune mode isentered. The process terminates at block 424. Returning to block 420, ifC_(min) is greater than the current cost C_(t), control proceeds toblock 406 or a fault is declared. The process then terminates at block424.

The various embodiments of the present disclosure address a controlbased approach that can be used to directly minimize the measuredreflected power or the normalized magnitude of the complex reflectioncoefficient |Γ| land, therefore, reflected power. The control basedapproach described herein can improve upon present approaches thatleverage intermediate or surrogate values, such as various electricalparameters and can arrive at less than optimal conditions or where thesurrogate measurement has not reached a minimum (or maximum) at anoperating point that does not correspond to minimum effected power.Further, the various embodiments of the present disclosure are directedto various auto frequency tuning approaches which do not require a modelof the plasma process. Rather, the auto frequency tune controllerdetermines required information based on the reaction of the system toan input perturbation signal that probes the output response as afunction of the input actuation signal. Thus, the various embodimentsdescribed herein are less sensitive to modeling errors presented byconventional control based approaches to auto frequency tuning. Further,the various embodiments provided herein requires no special calibration,and the tuner does not require any type of rotation or correction toimpedance values on the Smith chart to account for cable length or toorient the impedance trajectory to assist in proper tuning. Thus, unlikesearch-based methods, the disclosure described herein provides anadaptive control responsive to and compensating for a slow drift in theprocess. In various embodiments of the disclosure described herein, onlythe magnitude of the complex reflection coefficient |Γ| is required, ascompared to the complex reflection coefficient Γ. This simplifiescomputations required to perform auto frequency tuning. However, thevarious embodiments described herein also are operational withmeasurements from a direction coupler in addition to a VI probe.

In various embodiments, the RF signal or envelope is pulsed withmultiple pulse states (1 . . . n), an extremum seeking frequencycontroller can be applied to each pulse state, j, allowing very fast andstable transitions from one pulse state to the next. When a given pulsestate, j, terminates, the relevant state variables are saved andsubsequently restored when state j resumes. An example of such amultiple pulse state system can be found with respect to U.S. Pat. No.8,952,765 assigned to the assignee of the patent application andincorporated in their entirety by reference herein.

In various embodiments, where the pulsed RF signal or envelope ismodulated in a repeating pattern, the RF envelope can be divided into ptime segments or “bins”. An extremum seeking impedance controller can beapplied to each time segment. An example of such a system can be foundwith reference to U.S. Pat. Nos. 10,049,357 and 10,217,609, bothassigned to the assignee of the patent application and incorporated byreference herein.

As described above, in various embodiments, other impedance actuatorscan be used in place of frequency. By way of non-limiting example,matching network capacitance can be used as an impedance tuningactuator. In a typical L-type matching network, the series capacitor hasa similar effect on impedance as the amplifier frequency. Thecapacitance can be varied by several methods, including stepper motordriven vacuum variable capacitor, analog varactor, on/off switch, andphase shift impedance modulation.

The foregoing description is merely illustrative in nature and is in noway intended to limit the disclosure, its application, or uses. Thebroad teachings of the disclosure can be implemented in a variety offorms. Therefore, while this disclosure includes particular examples,the true scope of the disclosure should not be so limited since othermodifications will become apparent upon a study of the drawings, thespecification, and the following claims. It should be understood thatone or more steps within a method may be executed in different order (orconcurrently) without altering the principles of the present disclosure.Further, although each of the embodiments is described above as havingcertain features, any one or more of those features described withrespect to any embodiment of the disclosure can be implemented in and/orcombined with features of any of the other embodiments, even if thatcombination is not explicitly described. In other words, the describedembodiments are not mutually exclusive, and permutations of one or moreembodiments with one another remain within the scope of this disclosure.

Spatial and functional relationships between elements (for example,between modules, circuit elements, semiconductor layers, etc.) aredescribed using various terms, including “connected,” “engaged,”“coupled,” “adjacent,” “next to,” “on top of,” “above,” “below,” and“disposed.” Unless explicitly described as being “direct,” when arelationship between first and second elements is described in the abovedisclosure, that relationship can be a direct relationship where noother intervening elements are present between the first and secondelements, but can also be an indirect relationship where one or moreintervening elements are present (either spatially or functionally)between the first and second elements. As used herein, the phrase atleast one of A, B, and C should be construed to mean a logical (A OR BOR C), using a non-exclusive logical OR, and should not be construed tomean “at least one of A, at least one of B, and at least one of C.”

In the figures, the direction of an arrow, as indicated by thearrowhead, generally demonstrates the flow of information (such as dataor instructions) that is of interest to the illustration. For example,when element A and element B exchange a variety of information butinformation transmitted from element A to element B is relevant to theillustration, the arrow may point from element A to element B. Thisunidirectional arrow does not imply that no other information istransmitted from element B to element A. Further, for information sentfrom element A to element B, element B may send requests for, or receiptacknowledgements of, the information to element A.

In this application, including the definitions below, the term “module”or the term “controller” may be replaced with the term “circuit.” Theterm “module” may refer to, be part of, or include: an ApplicationSpecific Integrated Circuit (ASIC); a digital, analog, or mixedanalog/digital discrete circuit; a digital, analog, or mixedanalog/digital integrated circuit; a combinational logic circuit; afield programmable gate array (FPGA); a processor circuit (shared,dedicated, or group) that executes code; a memory circuit (shared,dedicated, or group) that stores code executed by the processor circuit;other suitable hardware components that provide the describedfunctionality; or a combination of some or all of the above, such as ina system-on-chip.

The module may include one or more interface circuits. In some examples,the interface circuits may include wired or wireless interfaces that areconnected to a local area network (LAN), the Internet, a wide areanetwork (WAN), or combinations thereof. The functionality of any givenmodule of the present disclosure may be distributed among multiplemodules that are connected via interface circuits. For example, multiplemodules may allow load balancing. In a further example, a server (alsoknown as remote, or cloud) module may accomplish some functionality onbehalf of a client module.

The term code, as used above, may include software, firmware, and/ormicrocode, and may refer to programs, routines, functions, classes, datastructures, and/or objects. The term shared processor circuitencompasses a single processor circuit that executes some or all codefrom multiple modules. The term group processor circuit encompasses aprocessor circuit that, in combination with additional processorcircuits, executes some or all code from one or more modules. Referencesto multiple processor circuits encompass multiple processor circuits ondiscrete dies, multiple processor circuits on a single die, multiplecores of a single processor circuit, multiple threads of a singleprocessor circuit, or a combination of the above. The term shared memorycircuit encompasses a single memory circuit that stores some or all codefrom multiple modules. The term group memory circuit encompasses amemory circuit that, in combination with additional memories, storessome or all code from one or more modules.

The term memory circuit is a subset of the term computer-readablemedium. The term computer-readable medium, as used herein, does notencompass transitory electrical or electromagnetic signals propagatingthrough a medium (such as on a carrier wave); the term computer-readablemedium may therefore be considered tangible and non-transitory.Non-limiting examples of a non-transitory, tangible computer-readablemedium are nonvolatile memory circuits (such as a flash memory circuit,an erasable programmable read-only memory circuit, or a mask read-onlymemory circuit), volatile memory circuits (such as a static randomaccess memory circuit or a dynamic random access memory circuit),magnetic storage media (such as an analog or digital magnetic tape or ahard disk drive), and optical storage media (such as a CD, a DVD, or aBlu-ray Disc).

In this application, apparatus elements described as having particularattributes or performing particular operations are specificallyconfigured to have those particular attributes and perform thoseparticular operations. Specifically, a description of an element toperform an action means that the element is configured to perform theaction. The configuration of an element may include programming of theelement, such as by encoding instructions on a non-transitory, tangiblecomputer-readable medium associated with the element.

The apparatuses and methods described in this application may bepartially or fully implemented by a special purpose computer created byconfiguring a general purpose computer to execute one or more particularfunctions embodied in computer programs. The functional blocks,flowchart components, and other elements described above serve assoftware specifications, which can be translated into the computerprograms by the routine work of a skilled technician or programmer.

The computer programs include processor-executable instructions that arestored on at least one non-transitory, tangible computer-readablemedium. The computer programs may also include or rely on stored data.The computer programs may encompass a basic input/output system (BIOS)that interacts with hardware of the special purpose computer, devicedrivers that interact with particular devices of the special purposecomputer, one or more operating systems, user applications, backgroundservices, background applications, etc.

The computer programs may include: (i) descriptive text to be parsed,such as HTML (hypertext markup language), XML (extensible markuplanguage), or JSON (JavaScript Object Notation) (ii) assembly code,(iii) object code generated from source code by a compiler, (iv) sourcecode for execution by an interpreter, (v) source code for compilationand execution by a just-in-time compiler, etc. As examples only, sourcecode may be written using syntax from languages including C, C++, C#,Objective-C, Swift, Haskell, Go, SQL, R, Lisp, Java®, Fortran, Perl,Pascal, Curl, OCaml, Javascript®, HTML5 (Hypertext Markup Language 5threvision), Ada, ASP (Active Server Pages), PHP (PHP: HypertextPreprocessor), Scala, Eiffel, Smalltalk, Erlang, Ruby, Flash®, VisualBasic®, Lua, MATLAB, SIMULINK, and Python®.

What is claimed is:
 1. A radio frequency (RF) generator comprising: a RFpower source configured to generate an output signal at an outputfrequency; and a frequency tuning module configured to generate afrequency control signal, the frequency control signal varying theoutput frequency of the RF power source, the frequency control signal isformed from a frequency tuning signal and a perturbation signal, whereinthe perturbation signal varies an electrical parameter of the outputsignal, and wherein the frequency tuning signal is adjusted inaccordance with a change in output signal in response to theperturbation signal.
 2. The RF generator of claim 1, wherein theelectrical parameter is at least one of voltage, current, forward power,reflected power, or a reflection coefficient.
 3. The RF generator ofclaim 1, wherein the frequency tuning signal varies an impedance betweenthe RF generator and a load.
 4. The RF generator of claim 1 comprising:a signal source, the signal source configured to generate theperturbation signal; a mixer configured to mix the perturbation signaland the electrical parameter to generate a mixed signal; a feedbackmodule, the feedback module configured to determine an updated frequencytuning signal in accordance with the mixed signal; and a signal combinerconfigured to combine the perturbation signal and the updated frequencytuning signal to generate an updated frequency control signal.
 5. The RFgenerator of claim 4 wherein, if the mixed signal is in phase with theperturbation signal, the electrical parameter is adjusted in a positivedirection toward a maximum, and if the mixed signal is out of phase withthe perturbation signal or negative, the electrical parameter isadjusted in a negative direction toward a maximum; or if the mixedsignal is in phase with the perturbation signal, the electricalparameter is adjusted in a negative direction toward a minimum, and ifthe mixed signal is out of phase with the perturbation signal, theelectrical parameter is adjusted in a positive direction toward aminimum.
 6. The RF generator of claim 5 wherein the feedback moduleincludes an integrator, wherein the integrator is configured to receiveand integrate the mixed signal and generates the frequency tuningsignal.
 7. The RF generator of claim 6 wherein the frequency tuningsignal increases or decreases in accordance with whether theperturbation signal and the mixed signal are in phase or out of phase.8. The RF generator of claim 4 further comprising: a sensor, the sensoris configured to measure the electrical parameter and generating asensor signal; and a scaling module configured to receive the sensorsignal and apply scaling terms to the sensor signal to generate a scaledsensor signal, wherein a version of the scaled sensor signal is input tothe mixer.
 9. The RF generator of claim 8 further comprising a filterconfigured to receive the scaled sensor signal and generating a filteredversion of the sensed signal to the mixer.
 10. A radio frequency (RF)generator comprising: a RF power source configured to generate an outputsignal at an output frequency; a frequency controller configured togenerate a frequency control signal, the frequency control signalvarying the output frequency of the RF power source, the frequencycontrol signal is formed from an impedance tuning signal and aperturbation signal, a signal source configured to generate theperturbation signal; a mixer configured to mix the perturbation signaland an electrical parameter to generate a mixed signal; a feedbackmodule, the feedback module is configured to determine an updatedfrequency tuning signal in accordance with the mixed signal; and asignal combiner configured to combine the perturbation signal and theupdated frequency tuning signal and to generate an updated frequencycontrol signal wherein the perturbation signal varies an electricalparameter of the output signal, and wherein the frequency control signalis adjusted in accordance with a change in output signal in response tothe perturbation signal, wherein the electrical parameter is at leastone of voltage, current, forward power, reflected power, or a reflectioncoefficient.
 11. The RF generator of claim 10, wherein the frequencycontrol signal varies an impedance between the RF generator and a load.12. The RF generator of claim 10 wherein, if the mixed signal is inphase with the perturbation signal, the electrical parameter is adjustedin a positive direction toward a maximum, and if the mixed signal is outof phase with the perturbation signal or negative, the electricalparameter is adjusted in a negative direction toward a maximum; or ifthe mixed signal is in phase with the perturbation signal, theelectrical parameter is adjusted in a negative direction toward aminimum, and if the mixed signal is out of phase with the perturbationsignal, the electrical parameter is adjusted in a positive directiontoward a minimum.
 13. The RF generator of claim 12 wherein the feedbackmodule includes an integrator, wherein the integrator is configured toreceive and integrate the mixed signal and generates the frequencycontrol signal.
 14. The RF generator of claim 13 wherein the frequencytuning signal increases or decreases in accordance with whether theperturbation signal and the mixed signal are in phase or out of phase.15. The RF generator of claim 12 further comprising a cost determinationmodule, the cost determination module is configured to determine one ofthe minimum or the maximum in accordance with a cost function determinedin accordance with a variation in frequency.
 16. The RF generator ofclaim 15 wherein the cost determination module is configured todetermine the frequency and a minimum cost associated with thefrequency.
 17. The RF generator of claim 12 wherein the perturbationsignal has a magnitude, and the magnitude of the perturbation signal isvaried in accordance with a magnitude of the electrical parameter. 18.The RF generator of claim 10 further comprising: a sensor, the sensor isconfigured to measure the electrical parameter and to generate a sensorsignal; and a scaling module configured to receive the sensor signal andapply scaling terms to the sensor signal to generate a scaled sensorsignal, wherein a version of the scaled sensor signal is input to themixer.
 19. A method for controlling a radio frequency (RF) generatorcomprising: generating an output signal at an output frequency; andgenerating a frequency control signal, the frequency control signalvarying the output frequency of a RF power source, the frequency controlsignal including a frequency tuning signal and a perturbation signal,wherein the perturbation signal varies an electrical parameter of theoutput signal, and wherein the frequency tuning signal is adjusted inaccordance with a change in the output signal in response to theperturbation signal.
 20. The method of claim 19, wherein the electricalparameter is at least one of voltage, current, forward power, reflectedpower, or a reflection coefficient.
 21. The method of claim 19 furthercomprising varying an impedance between the RF generator and a load byvarying the frequency of the frequency control signal.
 22. The method ofclaim 19 comprising: generating the perturbation signal; mixing theperturbation signal and the electrical parameter to generate a mixedsignal; determining an updated frequency tuning signal in accordancewith the mixed signal; and combining the perturbation signal and theupdated frequency tuning signal to generate an updated frequency controlsignal.
 23. The method of claim 22 wherein, if the mixed signal is inphase with the perturbation signal, adjusting the electrical parameterin a positive direction toward a maximum, and if the mixed signal is outof phase with the perturbation signal or negative, adjusting theelectrical parameter in a negative direction toward a maximum; or if themixed signal is in phase with the perturbation signal, adjusting theelectrical parameter in a negative direction toward a minimum, and ifthe mixed signal is out of phase with the perturbation signal, adjustingthe electrical parameter in a positive direction toward a minimum. 24.The method of claim 23 further comprising integrating the mixed signalto generate the frequency tuning signal.
 25. The method of claim 24further comprising increasing or decreasing the frequency tuning signalin accordance with whether the perturbation signal and the mixed signalare in phase or out of phase.
 26. The method of claim 22 furthercomprising: measuring the electrical parameter and generating a sensorsignal; and applying scaling terms to the sensor signal to generate ascaled sensor signal, wherein a version of the scaled sensor signal ismixed with the perturbation signal.